On the Quasiconcave Multilevel Programming Problems

H. Sadeghi and M. Esmaeili ()
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H. Sadeghi: Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
M. Esmaeili: Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Asia-Pacific Journal of Operational Research (APJOR), 2022, vol. 39, issue 03, 1-15

Abstract: Multilevel programming appears in many decision-making situations. Investigation of the main properties of quasiconcave multilevel programming (QCMP) problems, to date, is limited to bilevel programming (only two levels). In this paper, first, we present an extension of the properties of quasiconcave bilevel programming (QCBP) problems for the case when three levels exist. Then, by induction on n (the number of levels), we prove the existence of an extreme point of the polyhedral constraint region that solves the QCMP problem under given conditions. Ultimately, a number of numerical examples are illustrated to verify the results.

Keywords: Extreme points; trilevel programming; multilevel programming; quasiconcave functions; optimal solutions (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0217595921500263

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